There are two risks here:
- Sounding insulting (as you have noticed)
- Being boring (by bringing up some trivial thing from a year ago)
You should avoid both, because there is nothing to gain from emphasizing them.
Dear [name], lately I've been working on my current [paper/research/assignment] and here's some updates on how that is going. We can talk in more detail in our next meeting.
Incidentally, I ended up learning [thing], which we had discussed in the past. It was interesting to find out that [implication].
I think this is a better answer than the accepted one because:
- Doesn't remind the professor that he "didn't know" (if it's been a year since, you may even be remembering wrong and perhaps he did know)
- Doesn't sound petty by referencing something from a year ago
- Isn't wasting his time with some random thing that hasn't been relevant in a year
- Sticks to relevant, pertinent things that matter to the work that's here and now, not ancient history
There is of course nothing wrong with discussing history. Sometimes there are unanswered questions that linger for decades or centuries before spurning great discoveries when their time comes. But a productive researcher should maintain focus on priorities. If this thing from a year ago was that important, a year ago wouldn't have been the last time you discussed it. So one has to wonder, if nobody's cared in a year, why should anyone start now? I think answering that question is the most constructive direction to go here.
I wrote the above assuming you have a relationship with the professor already. If you are talking about an undergraduate instructor, the same principles still hold, but a better example template could be:
I have decided to work on [problem], and I wanted to share my findings with you. I actually became interested in this problem due to a discussion we had during our [class]. I have found that [answer], which is [implications].